US 20060031024 A1 Abstract A method of optimizing parameter values in a process, which process is essentially controlled by a set of parameters affecting a set of properties characterizing an output of the process. The method may use an analytic hierarchy process (AHP) to associate a weight with each property according to its relative importance to obtain desired product characteristics. The method also uses parameter data and measured property data from a required number of experimental runs of the process, from which data property behavior relations between each property and the parameters are statistically established, which relations give estimated property values. Using the property weights, a process goal function is established, which is expressed in terms of weighted deviations between the estimated property values and the corresponding goal values for the properties. The process goal function is minimized in order to generate a set of optimal parameter values for the process.
Claims(5) 1. A method of optimizing parameter values of a process, the process being essentially controlled by a set of n parameters X that affect a set of k properties Y characterizing an output of the process, said method comprising:
assigning values to a set of k property weights representing relative importance of said properties; establishing property behavior mathematical relations giving an estimated property for each said property; using said property weights to establish a goal function in terms of property weighted deviations between the estimated properties and corresponding specified goal values for said properties; and minimizing the goal function to generate a set of n optimal parameter values for said parameters. 2. A method according to 3. A method according to 4. A method according to 5. An apparatus capable of optimizing parameter values of a process, the process being essentially controlled by a set of n parameters X that affect a set of k properties Y characterizing an output of the process, said apparatus comprising:
means for assigning values to a set of k property weights representing relative importance of said properties; means for establishing property behavior mathematical relations giving an estimated property for each said property; means for using said property weights to establish a goal function in terms of property weighted deviations between the estimated properties and corresponding specified goal values for said properties; and means for minimizing the goal function to generate a set of n optimal parameter values for said parameters. Description 1. Field of the Invention The invention relates to the process optimization field, and more particularly to a method of optimizing parameter values in a process of producing a product which is characterized by properties affected by the selected parameter values. This invention is applicable in different industries, such as the pharmaceutical, chemical, cosmetics, plastics, petrochemical, agriculture, metallurgy and food industries, as well as many other commercial and industrial applications. 2. Description of Prior Art Processes for production of complex compositions such as those found in many pharmaceutical products generally require the mixing of many ingredients according to specific process parameters regarding formulation and production technology, to provide the product with properties at a level offering satisfactory performance according to predetermined specifications. In such complex production processes, it is not unusual that some process parameters involved exhibit interfering effects on the desired properties, further complicating the process design. Where possible, the designer may try to adapt the set of process parameters from known data derived from previous similar processes, and/or rely on conventional trial-and-error experimental schemes to optimize the set of process parameters values, in order to meet the product specifications. However, as the processes become more complex, optimization in such multidimensional space with high accuracy requirements turns out to be an extremely difficult task, even for the highly skilled designer. That limitation is particularly problematic in the design of pharmaceutical products, where one or more active substances mixed with a variety of excipients (e.g. carriers) must be produced in the form of a stable and highly effective standard delivery system such as a tablet, capsule, suspension, cream or injection, or even controlled release systems such as skin carriers and implants. In the past years, many techniques have been developed to assist the process designer or formulator in optimizing values of parameters governing processes. These techniques aim at quantify existing relations between parameters and associated desired product performance characteristics. A conventional technique known as the Full Factorial Matrix (FFM) method consists of statistically deriving a behavior relations for the properties from a set of experimental runs of the process using selected initial values for the parameters. The established model being generally nonlinear, optimized parameter values are then derived using an optimization method such as the Multisimplex method described in “ The known optimization processes based on Full Factorial Matrix-Multisimplex methods suffer from several drawbacks. As a general rule, the number of experimental runs required to obtain a model of sufficient reliability is proportional to the total number of significant parameters involved. Therefore, the cost and time frame of the experimental work will therefore be essentially proportional to the number of runs required. Although a variant of the method known as the Fractional Factorial Matrix has been proposed in order to reduce the number of runs to be performed, the provided reduction of experimental runs may not significantly reduce the total cost and time frame of the work required to complete the design of a complex product involving many production technologies. While adequate formulations complying with constraints imposed on the parameter values can nevertheless be obtained, these formulations generally cannot be qualified as optimal when comparing actual property performance with desired property values set forth in the product specifications. A technique which attempts to improve parameter optimization in process design is disclosed in European Patent Office laid-open patent application publication number 0,430,753 dated Jun. 5, 1991 and in U.S. Pat. No. 5,218,526 issued on Jun. 8, 1993 to Mozzo. According to the technique in Mozzo, from a set of property relations expressed in terms of parameters which is obtained by standard statistical methods using the results of a number of experimental runs of the process, a corresponding set of property relations expressed in terms of weighted parameters is derived. For each actual value of a parameter, a first weighting is expressed as the ratio of: (a) the deviation of the actual value from the mean value of the parameter over the experimental range, on (b) the range between extreme values for that parameter over the experimental range. Then, a goal function is established in term of deviations between weighted values of property values as estimated by the property relations and corresponding weighted values of specified goal values for the properties. For each goal value of a property, a second weighting is expressed as the ratio of: (a) the deviation of the actual value from the mean value of the property over the experimental range, on (b) the range between extreme values for that property over the experimental range. Then, according to a recursive geometric algorithm aimed at successively minimizing the established goal function, a set of optimal parameter values is generated. While being an improvement over the conventional Full/Fractional Factorial Matrix—Multisimplex methods regarding the capability to consider specified goal values for the properties, the weightings as taught by Mozzo do not reflect the relative importance of the properties involved, and that limitation may therefore affect the convergence of the algorithm toward an optimal solution. A review of modern techniques and software systems for the design of pharmaceutical product formulations is given in “ It is therefore an object of the present invention to provide a systematic method of optimizing parameter values in a process for producing a product which minimizes the number of experimental runs required to obtain an optimal solution complying with the product specifications. According to the above object, from a broad aspect of the present invention, there is provided a method of optimizing parameter values in a process of producing a product, the process being essentially controlled by a set of n parameters X According to a further broad aspect of the present invention, there is provided a method of producing a pharmaceutical product using optimized process parameter values, the process being essentially controlled by a set of n parameters X The invention will be better understood by way of the following detailed description of a preferred embodiment with reference to the appended drawings, in which: In the following description, a preferred embodiment of the present invention applied to product formulation design will be described. However, it is to be understood that the present invention can be also be used to optimize parameter values of processes related to the production of many types of products which cannot be associated with a formulation, while being characterized by a number of properties affected by process parameters, such as biotechnological products, electronic components, etc. Referring now to Modules An optimization module A preferred embodiment of an optimization method according to the present invention will now be described with reference to The AHP method consists of building a hierarchical tree from all properties, with one or more hierarchical levels depending on existing relations between the properties. For each level, a pair-wise comparison matrix is built between the properties of this level and presented at an input of the parameters weighting module In a parallel direction, each pair-wise comparison is associated with a consistency index reflecting the transitivity relation between all comparison by pairs given by the formulator. Multi-criteria analysis software which is commercially available, such as Expertchoice™, Criterium™ or Ergo™, may be used to program module According to the next step, namely step The method then comprises a step The parameters associated with the retained correlation factors form the reduced set of n parameters. It can be also shown that a minimum number l of runs at least equal to n+1 is required to obtain reliable parameters estimation. Then, parameter interactions, that are in the form X A following step The goal function to be minimized may be expressed as follows:
The “G” goal function is determinated by experimentation. The optimization of the “G” function is a step by step procedure. The first step is to obtain the behavior laws with the best fit between the experimental data and their corresponding ideal value factor. The second step, the optimization is based on a initial point.
g= H=the Hessian of G
We observe a perfect overlap between the two goal functions and on the stationary point the goal function will be;
These equations supply the maxima and minima of the goal
This mathematical approach induces a reduction of the dimension of the variables, consequently we pass from “n” variables to “n−1” variables. In the actual case, we start with the most important variables from the behavior laws with the highest weight values of the factor. This approach is known under the name of network optimization, in this case the network nodes are built by the optimal values of the variable by decreasing order of the factor's rank. After the iterative optimization step An example illustrating an application of the method according to the present invention in the pharmaceutical field will now be described. Formulation and production process for enalapril maleate tablets were optimized in order to provide a drug product with satisfactory biological performance as well as stability when packaged and stored under ICH (International Conference on Harmonization) conditions. Three (3) independent formulation and process parameters (n=3) were identified as having an impact on the stability of the drug product: 1) the degree of drug neutralization during granulation (X As to the degree of drug neutralization during granulation (X The manufacturing technology (X As to the dose strength (X A total of nine (9) experimental runs involving different formulations based on a combination of the three parameters were prepared, as shown in Table 1.
The nine formulations covered all of the six (6) possible combinations for the wet granulation technology and three (3) combinations of direction compression. Tablets were manufactured by using enalapril maleate with USP/NF and EP excipients. In the direct compression technology, there is not a sufficient amount of moisture to dissolve all the drug and alkaline agent and provide for any significant neutralization reaction. However, excipients do contain a certain level of adsorbed free moisture capable of creating a microenvironment where small quantities of the drug and alkaline agent can be dissolved and become available for the neutralization reaction. These phenomena could be responsible of the appearance of physical as well as chemical stability problems and where taken into account by evaluating three (3) formulation combinations. The nine (9) formulation combinations where prepared and the tablets were stored in opened containers at 25° C./60% RH and 40° C./75% RH for a 2-week period. These open container studies are typically conducted during the early formulation development phases of a product to purposely accelerate physical and chemical changes in formulations in order to select the lead candidate, i.e., the formulation with the best stability profile. After the 2-week time period, the tablets were removed from the environmental chambers and sent to the analytical department for their performance evaluation. The performance of the formulations was determined by measuring ten (k=10) properties as a function of time and temperature, which properties were selected as follows, according to a hierarchical tree comprising properties and sub-properties: - Y11, Y12, Y13: % drug dissolved at 5, 15, and 30 min. (sub-properties of Y1);
- Y2: % of cyclization product at time zero;
- Y31, Y32: % cyclization product after 2 weeks at 25° C./60% RH and at 40° C./75% RH (sub-properties of Y3);
- Y4: differential between theoretical and actual assay in mg at time zero;
- Y51, Y52: differential between theoretical and actual assay in mg after 2 weeks at 25° C./60% RH and at 40° C./75% RH (sub-properties of Y5);
- Y6: % hydrolytic product after 2 weeks at 40° C./75%.
Applying the AHP process with the standard scale for these properties, the decision matrixes given in Table 2 for the properties and in Tables 3, 4 and 5 for the sub-properties were built.
From the decision matrixes, the following weight values for the k=10 properties/sub-properties are given in Table 6, the sum of the weights being equal to unity.
Experimental property data that were obtained from nine (9) runs of the process using the selected nine (9) combinations of parameter values of Table 1, are given in Table 7.
Since n=3<8, the parameter reduction step is not required for the purpose of the instant case. As to the statistical analysis of parameters interaction, since a correlation factor ρ The specified goal values for the properties as given in Table 8 were used to establish the goal function that was minimized to generate the following set of optimal parameters:
The associated experimental property values are given in Table 9.
Applying the method for the particular case where only the minimum four (n+1=3+1=4) experimental runs required were used, runs 1, 3, 6 and 9 were selected to provide the parameter and property data as given in Table 7. As to the statistical analysis of parameters interaction, since a correlation factor ρ The same specified goal values for the properties as given in Table 8 were used to establish the goal function that was minimized to generate the following set of optimal parameters:
The associated experimental property values are given in Table 10.
Comparing the set of parameter values given at (20) with the former set obtained from all nine (9) experimental runs given at (19), it can be noted that both sets are very similar. Actually, from a pharmaceutical standpoint, they could almost be considered as identical. Referenced by
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